1. Which is the best method to use to solve two simultaneous equations?
With two linear equations, there are 4 methods to choose from depending on the way each of the two equations are arranged.
With a linear and a non-linear equation, such as a parabola, a substitution method is usually the best.
2. Is the graphical method a good way of solving simultaneous equations?
If the solution set is two integers e.g. (1, -2) the values are easy to read from a graph but if not, it can be difficult to get accurate values.
Thinking about the graphs is a good way to check your answers,
3. Which are the two most commonly used methods for solving simultaneous equations?
The elimination method and the substitution method are the most commonly used methods for solving simultaneous equations where both equations are linear.
For other combinations of equations the substitution method is probably the easiest and most common.